{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30 30\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.arange(1.1,4.1,0.1)\n",
    "y=np.array([8.0725, 5.2761, 3.8791, 3.0955, 2.6103, 2.2853, 2.0541, 1.8822, 1.7497, 1.6449, \n",
    "            1.5602, 1.4905, 1.4324, 1.3833, 1.3414, 1.3054, 1.2742, 1.2470, 1.2231, 1.2020,\n",
    "            1.1833, 1.1667, 1.1519, 1.1386, 1.1267, 1.1159, 1.1062, 1.0975, 1.0895, 1.0823 ])\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.51510508 -0.54270779  1.60764036]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\python27\\lib\\site-packages\\ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in power\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.arange(1.1,4.1,0.1)\n",
    "y=np.array([8.0725, 5.2761, 3.8791, 3.0955, 2.6103, 2.2853, 2.0541, 1.8822, 1.7497, 1.6449, \n",
    "            1.5602, 1.4905, 1.4324, 1.3833, 1.3414, 1.3054, 1.2742, 1.2470, 1.2231, 1.2020,\n",
    "            1.1833, 1.1667, 1.1519, 1.1386, 1.1267, 1.1159, 1.1062, 1.0975, 1.0895, 1.0823 ])\n",
    "def f(x,a,b,c):\n",
    "    return np.power((c/1.0/(a*x+b)),0.5)\n",
    "\n",
    "fita,fitb=optimize.curve_fit(f,x,y)\n",
    "print(fita)\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,f(x,fita[0],fita[1],fita[2]))\n",
    "# plt.plot(x,f(x,0.5,-0.55,1.6))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
